I just want to echo the tips above about getting your teammates involved and communicating your intentions to them. I play defense, but my team's top center wins a ton of his draws by mixing things up and getting our teammates involved.

I mention communication because our team's top center will do things differently given the situation (win it to a winger, chip it behind the net and have a wing chase it down, tie up the other center and pray, etc.) and he's always sure to let the wingers know before hand. But in those situations were I am on the ice and we get a face-off, almost every time he goes for a back-hand sweep back to me on defense. At which point I go for a quick shot off the face-off win (in the offensive zone) or I position myself to receive the puck and carry it around the net (in the defensive zone). Teams might pay attention to the tendencies of a center, but the roles of even specific teammate combinations can throw unexpected results into the mix.